Appendix S1

Estimating Carrying Capacity for Chinook Parr using Quantile Random Forest Models

¹ Biomark, Inc. 705 South 8th St., Boise, Idaho, 83702, USA

^✉ Correspondence: Kevin E. See <Kevin.See@biomark.com>

Choosing Habitat Covariates

A key step in developing a QRF model to predict fish capacities was selecting the habitat covariates to include in the model. Random forest models naturally incorporate interactions between correlated covariates, which is essential since nearly all habitat variables are considered correlated to one degree or another, however, we aimed to avoid overly redundant variables (i.e., variables that measure similar aspects of the habitat). Further, including too many covariates can result in overfitting of the model (e.g., including as many covariates as data points).

To prevent overfitting, we pared down the more than 100 metrics generated by the CHaMP protocol describing the quantity and quality of fish habitat for each survey site. To assist in determining the habitat metrics to include in the QRF model, we used the Maximal Information-Based Nonparametric Exploration (MINE) class of statistics (Reshef et al. 2011) to determine those habitat characteristics (covariates) most highly associated with observed parr densities. We calculated the maximal information coefficient (MIC), using the R package minerva (Filosi et al. 2019), to measure the strength of the linear or non-linear association between two variables (Reshef et al. 2011). The MIC value between each of the measured habitat characteristics and parr density was used to inform decisions on which habitat covariates to include in the QRF parr capacity model.

Habitat metrics were first grouped into broad categories that included channel unit, complexity, cover, disturbance, riparian, size, substrate, temperature, water quality, and woody debris. Habitat metrics measuring volume or area were scaled to the wetted area of each site. Within each category, metrics were ranked according to their MIC value (Table 1 and Figure 1). Our strategy was to select one or two variables with the highest MIC score within each category so that covariates describe different aspects of rearing habitat (e.g., substrate, temperature, etc.). Additionally, we attempted to avoid covariates that were highly correlated (Figure ??) while including covariates that can be directly influenced by restoration actions or have been shown to impact salmonid juvenile density.

References

Filosi, M., R. Visintainer, and D. Albanese. 2019. Minerva: Maximal information-based nonparametric exploration for variable analysis.

Reshef, D. N., Y. A. Reshef, H. K. Finucane, S. R. Grossman, G. McVean, P. J. Turnbaugh, E. S. Lander, M. Mitzenmacher, and P. C. Sabeti. 2011. Detecting novel associations in large data sets. Science 334:1518–1524.

Tables

Table 1: MIC statistic for top metrics in each habitat category. Metrics selected for the QRF model are in bold.

Category	Name	Abbrv	MIC
ChannelUnit	Channel Unit Frequency	CU_Freq	0.241
ChannelUnit	Fast Turbulent Frequency	FstTurb_Freq	0.230
ChannelUnit	Fast NonTurbulent Frequency	FstNT_Freq	0.209
ChannelUnit	Slow Water Frequency	SlowWater_Freq	0.208
ChannelUnit	Fast Turbulent Percent	FstTurb_Pct	0.195
ChannelUnit	ChnlUnitTotal_Ct	ChnlUnitTotal_Ct	0.189
ChannelUnit	Channel Unit Count	CU_Ct	0.189
ChannelUnit	Fast Turbulent Count	FstTurb_Ct	0.178
ChannelUnit	Slow Water Percent	SlowWater_Pct	0.177
ChannelUnit	Fast NonTurbulent Percent	FstNT_Pct	0.169
Complexity	Wetted Width To Depth Ratio Avg	WetWDRat_Avg	0.247
Complexity	Bankfull Width To Depth Ratio Avg	BfWDRat_Avg	0.245
Complexity	Wetted Depth SD	DpthWet_SD	0.232
Complexity	Wetted Channel Braidedness	WetBraid	0.212
Complexity	Bankfull Channel Braidedness	BfBraid	0.211
Complexity	Wetted Channel Qualifying Island Count	Wet_QIsland_Ct	0.209
Complexity	Bankfull Width CV	BfWdth_CV	0.209
Complexity	Bankfull Width To Depth Ratio CV	BfWDRat_CV	0.202
Complexity	Detrended Elevation SD	DetrendElev_SD	0.196
Complexity	Bankfull Channel Qualifying Island Count	Bf_QIsland_Ct	0.193
Cover	Fish Cover: Total	FishCovTotal	0.225
Cover	Fish Cover: None	FishCovNone	0.224
Cover	Fish Cover: LW	FishCovLW	0.213
Cover	Fish Cover: Terrestrial Vegetation	FishCovTVeg	0.204
Cover	Percent Undercut by Length	UcutLgth_Pct	0.185
Cover	Percent Undercut by Area	UcutArea_Pct	0.184
Cover	Fish Cover: Aquatic Vegetation	FishCovAqVeg	0.166
Cover	Fish Cover: Artificial	FishCovArt	0.136
Land Classification	Natural Class PCA 2	NatPrin2	0.271
Land Classification	Natural Class PCA 1	NatPrin1	0.258
Land Classification	Disturbance Class PCA 1	DistPrin1	0.242
Riparian	Riparian Cover: Understory	RipCovUstory	0.206
Riparian	RipCovUstoryNone	RipCovUstoryNone	0.206
Riparian	Riparian Cover: No Canopy	RipCovCanNone	0.194
Riparian	Riparian Cover: Some Canopy	RipCovCanSome	0.194
Riparian	Riparian Cover: Big Tree	RipCovBigTree	0.184
Riparian	Riparian Cover: Ground	RipCovGrnd	0.182
Riparian	RipCovGrndNone	RipCovGrndNone	0.170
Riparian	Riparian Cover: Woody	RipCovWood	0.168
Riparian	Riparian Cover: Non-Woody	RipCovNonWood	0.166
Riparian	Riparian Cover: Coniferous	RipCovConif	0.164
SideChannel	Bankfull Side Channel Width	BfSCWdth	0.223
SideChannel	Wetted Side Channel Width	WetSCWdth	0.213
SideChannel	Wetted Side Channel Percent By Area	WetSC_Pct	0.209
SideChannel	SCSm_Freq	SCSm_Freq	0.153
SideChannel	SCSm_Ct	SCSm_Ct	0.153
SideChannel	SC_Area_Pct	SC_Area_Pct	0.153
Size	Mean Annual Flow	MeanU	0.346
Size	Wetted Width Integrated	WetWdth_Int	0.332
Size	Bankfull Width Integrated	BfWdthInt	0.324
Size	Wetted Width Avg	WetWdth_Avg	0.324
Size	Drainage Area (Flowline)	CUMDRAINAG	0.302
Size	Bankfull Width Avg	BfWdth_Avg	0.298
Size	DpthThlwg_Avg	DpthThlwg_Avg	0.280
Size	Discharge	Q	0.259
Size	Bankfull Depth Avg	DpthBf_Avg	0.245
Size	Bankfull Depth Max	DpthBf_Max	0.240
Substrate	Substrate < 6mm	SubLT6	0.237
Substrate	Substrate < 2mm	SubLT2	0.227
Substrate	Substrate: D16	SubD16	0.219
Substrate	Substrate: Embeddedness Avg	SubEmbed_Avg	0.204
Substrate	Substrate: D50	SubD50	0.197
Substrate	Substrate Est: Sand and Fines	SubEstSandFines	0.190
Substrate	Substrate Est: Cobbles	SubEstCbl	0.185
Substrate	Substrate: D84	SubD84	0.185
Substrate	Substrate Est: Boulders	SubEstBldr	0.183
Substrate	Substrate: Embeddedness SD	SubEmbed_SD	0.181
Temperature	Avg. August Temperature	avg_aug_temp	0.272
Temperature	Elev_M	Elev_M	0.262
Temperature	August Temperature	aug_temp	0.188
Temperature	Solar Access: Summer Avg	SolarSummr_Avg	0.186
WaterQuality	Conductivity	Cond	0.254
WaterQuality	Alkalinity	Alk	0.225
WaterQuality	Drift Biomass	DriftBioMass	0.000
Wood	Large Wood Volume: Bankfull Slow Water	LWVol_BfSlow	0.213
Wood	Large Wood Volume: Wetted Slow Water	LWVol_WetSlow	0.207
Wood	Large Wood Frequency: Wetted	LWFreq_Wet	0.199
Wood	Large Wood Volume: Bankfull	LWVol_Bf	0.189
Wood	Large Wood Volume: Wetted Fast Turbulent	LWVol_WetFstTurb	0.187
Wood	Large Wood Frequency: Bankfull	LWFreq_Bf	0.178
Wood	Large Wood Volume: Bankfull Fast NonTurbulent	LWVol_BfFstNT	0.175
Wood	Large Wood Volume: Wetted	LWVol_Wet	0.166
Wood	Large Wood Volume: Wetted Fast NonTurbulent	LWVol_WetFstNT	0.159

Figures

Figure 1: Barplots of MIC statistics, faceted by habitat category.

Figure 2: Barplot of MIC statistics, colored by habitat category.

Figure 3: Correlation plots of metrics, facted by habitat category.

Figure 4: Correlation plot of habitat metrics used in QRF model.

Figure 5: Pairs plot of habitat metrics used in QRF model with a correlation coefficient greater than 0.5.